ScalingStacks

Corollary 2.4. The canonical functor

$$\BTop(n)\longrightarrow\mathcal{E}{\sf uc}_{n}$$

is an equivalence of $\infty$-categories. In particular, there is a preferred equivalence of $\infty$-categories

$$\Psh(\mathcal{E}{\sf uc}_{n})~\simeq~\spaces_{/\BTop(n)}$$

between space-valued presheaves on $\mathcal{E}{\sf uc}_{n}$ and spaces over $\BTop(n)$.